Question

an alligators tail length is proportional to its body length. an alligator with a body length of 7.4 feet has a tail length of 8.3 feet. what is the tail length of an alligator whose body length is 3.1 feet? (round to two decimal places as needed.) complete the proportion, where the ratios have tail lengths in the numerators and body lengths in the denominators. (\frac{x}{square}=\frac{square}{square}) (do not simplify.) the tail length of an alligator whose body length is 3.1 feet is approximately (square) feet.

Explanation:

Step1: Set up the proportion

Let the body - length be $b$ and the tail - length be $t$. We know that $\frac{t_1}{b_1}=\frac{t_2}{b_2}$. Given $b_1 = 7.4$ feet, $t_1 = 8.3$ feet and $b_2=3.1$ feet. The proportion is $\frac{8.3}{7.4}=\frac{x}{3.1}$.

Step2: Cross - multiply

Cross - multiplying gives us $7.4x=8.3\times3.1$.
First, calculate $8.3\times3.1 = 25.73$. So, $7.4x = 25.73$.

Step3: Solve for $x$

Divide both sides of the equation $7.4x = 25.73$ by $7.4$. We have $x=\frac{25.73}{7.4}$.
$x\approx3.48$

Answer:

$3.48$